Casio ALGEBRA FX 2.0 Plus Instruction and safety manual

20010102
Computer Algebra
System and Tutorial
Modes (ALGEBRA FX 2.0 PLUS only)
7-1 Using the CAS (Computer Algebra System) Mode
7-2 Algebra Mode
7-3 Tutorial Mode
7-4 Algebra System Precautions
Chapter
7
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7-1-1
Using the CAS (Computer Algebra System) Mode
7-1 Using the CAS (Computer Algebra System)
Mode
On the Main Menu, select the CAS icon to enter the CAS Mode.
The following table shows the keys that can be used in the CAS Mode.
kk
kk
kInputting and Displaying Data
Input in the Algebra Mode is performed in the upper part of the display, which is called the
“input area.” You can input commands and expressions at the current cursor location.
Calculation results appear in the lower part of the display, which is called the “output area.”
When a calculation produces an equation or inequality, the lower part of the display is
divided between a “natural result display area” for the result, and a “formula number area” for
the formula number as shown below.
REPLAY
COPY PASTE
H-COPY
i

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If all the result does not fit on the display, use the cursor keys to scroll it.
kInputting List Data
List: {element, element, ..., element}
•Elements should be separated by commas, and the entire set of elements should be
enclosed within {curly braces}.
•You can input numeric values and expressions, equations, and inequalities as list elements.
○○○○○
Example To input List {1, 2, 3}
!*( { )b,c,d
!/( } )w
kInputting Matrix Data
Matrix (m×n): [[(1,1) entry, (1,2) entry, ..., (1,m) entry] [(2,1) entry, ......, (2,n) entry]...
[(m,n) entry, ..., (m,n) entry]]
•The above input is arranged to show the relative positions of entries in the matrix. Actual
input is an unbroken line, from left to right.
•Entries should be separated by commas, and the entire set of elements should be enclosed
within [square brackets]. And each line also should be enclosed within [square brackets].
•You can input numeric values and expressions as matrix entries.
○○○○○
Example To input the matrix shown below 1 2 3
4 5 6
7 8 9
!+( [ )!+( [ )b,c,d
!-( ] )!+( [ )e,f,g
!-( ] )!+( [ )h,i,j
!-( ] )!-( ] )w
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Using the CAS (Computer Algebra System) Mode
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7-1-3
Using the CAS (Computer Algebra System) Mode
kInputting Vector Data
Vector: [component, component, ..., component]
•Components should be separated by commas, and the entire set of components should be
enclosed within [square brackets].
•You can input numeric values and expressions as vector component entries.
○○○○○
Example To input Vector (1 2 3)
!+( [ )b,c,d
!-( ] )w
kk
kk
kPerforming an Algebra Mode Operation
There are two methods that you can use for input in the Algebra Mode.
•Function menu command input
•Manual formula and parameter input
kk
kk
kMenu Command Input
Press a function menu key to display the menu of functions for the type of operation you are
trying to perform.
•TRNS ... {formula transformation menu}
•CALC ... {formula calculation menu}
•EQUA ... {equation, inequality menu}
•eqn ... {calls up an equation stored in Equation Memory in accordance with a specified
input value}
•CLR ... {variable/formula delete menu}
Pressing the Kkey displays the menu shown below.
•LIST ... {list calculation menu}
•MAT ... {matrix calculation menu}
•VECT ... {vector calculation menu}
For details on commands and their formats, see the “Algebra Command Reference” on
page 7-1-11.
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kk
kk
kManual Formula and Parameter Input
You can use the function menus, Kkey, and Jkey in combination to input formulas and
parameters as described below.
•3(EQUA)b(INEQUA)
•{>}/{<}/{tt
tt
t}/{ss
ss
s} ... {inequality}
•Kkey
•{∞}/{Abs}/{x!}/{sign} ... {infinity}/{absolute value}/{factorial}/{signum function*1}
•{HYP} ... {hyperbolic}/{inverse hyperbolic} functions
•{sinh}/{cosh}/{tanh}/{sinh–1}/{cosh–1}/{tanh–1}
•Jkey
•{Yn}/{rn}/{Xtn}/{Ytn}/{Xn}... input of graph memory {Yn}/{rn}/{Xtn}/{Ytn}/{Xn}
kFormula Memory
The CAS Mode has 28 formula variables. Variable names are the letters A through Z, plus r,
and θ . CAS Mode formula variables are independent of standard value variables.
○○○○○
Example To assign a formula that differentiates sin(X) at X (cos(X)) to variable A
2(CALC)b(diff)sv,
v)aav(A)w
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Using the CAS (Computer Algebra System) Mode
1 (real number, A> 0)
–1 (real number, A< 0)
*1signum (A)A(A= imaginary number)
|A|
Undefined (A= 0)
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○○○○○
Example To assign M to row 1 column 2 of variable A when the matrix
is assigned to it
ah(M)aav(A)
!+( [ )b,c!-( ] )w
○○○○○
Example To recall the value of variable A when the list {X,Y, Z} is assigned to it
av(A)w
○○○○○
Example To recall the first component (A [1]) of variable A when vector (X Y Z) is
assigned to it
av(A)!+( [ )b
!-( ] )w
7-1-5
Using the CAS (Computer Algebra System) Mode
123
XYZ

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kFunction Memory and Graph Memory
Function memory lets you store functions for later recall when you need them.
With graph memory, you can store graphs in memory. Press the Jkey and then input the
name of the graph.
○○○○○
Example To differentiate f1= cos(X), which is assigned to function memory f1,
at X
2(CALC)b(diff)K6(g)4(FMEM)
d(fn)b,v)w
○○○○○
Example To differentiate Y1 = cos(X), which is assigned to graph memory Y1,
at X
2(CALC)b(diff)
J1(Yn) b,v)w
kEqn Memory
When a calculation result is an equation or inequality, its formula number is displayed in the
formula number area, and the equation is stored in Eqn memory.*1Stored equations can be
recalled with the eqn command, rclEqn command or rclAllEqn command.
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Using the CAS (Computer Algebra System) Mode
*1Up to 99 formulas can be stored in Eqn
memory.
The error message “Memory ERROR” when
you try to store an equation when there are
already 99 equations in Eqn memory. When
this happens, execute the ALLEQU (Delete
All Equations) from the CLR menu.
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kAnswer (Ans) Memory and Continuous Calculation
Answer (Ans) memory and continuous calculation can be used just as with standard
calculations. In the Algebra Mode, you can even store formulas in Ans memory.
○○○○○
Example To expand (X+1)2and add the result to 2X
1(TRNS)b(expand)
(v+b)x)w
Continuing:
+cvw
kReplay Contents
Replay memory can be used in the input area. After a calculation is complete, pressing d
or ein the input area recalls the formula of the last calculation performed. After a
calculation or after pressing A, you can press for cto recall previous formulas.
kMoving the Cursor Between Display Areas
When ]'`$indicates a calculation result that does not fit on the display, the cursor
keys perform output area scrolling. To use the Replay Function from this condition, press
6(g)2(SW). ]'`$change to a dotted line display to indicate that cursor key
operations control the input area.
Pressing 2(SW) again moves the cursor back to the output area.
7-1-7
Using the CAS (Computer Algebra System) Mode
# Pressing 6(g)1(CLR)d(ALLEQU)
deletes Eqn memory, Ans memory, and
Replay memory contents.
#You can input up to 255 bytes of data into the
input area.

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SET UP Items
uu
uu
uAngle ... Unit of angular measurement specification
•{Deg}/{Rad} ... {degrees}/{radians}
uu
uu
uAnswer Type ... Result range specification
•{Real}/{Cplx}... {real number}/{complex number}
uu
uu
uDisplay ... Display format specification (for approx only)
•{Fix}/{Sci}/{Norm}... {number of decimal places}/{number of significant digits}/
{normal display format}
kGraph Function
Pressing 5(GRPH) displays the graph formula screen, which you can use to input a graph
formula. Press 4(G
•
VAR) if you want to input a graph memory.
You can also use the 1(SEL), 2(DEL), and 3(TYPE) functions while the graph formula
screen is on the display.
Press 6(DRAW) to draw a graph.
kRECALL ANS Function
Pressing 6(g)3(R
•
ANS) recalls Ans Memory contents.
kSolution Memory
In the CAS Mode or ALGEBRA Mode, you can save the history of a calculation you perform
(replay memory contents) into solution memory. This section describes how you can access
and work with the contents of solution memory. Pressing 6(g)4(MEM) on the CAS Mode
or ALGEBRA Mode main menu display the initial solution memory screen shown below.
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Using the CAS (Computer Algebra System) Mode
•{SAVE} ... {saves the calculation history to solution memory}
•{DEL
•
A}... {deletes solution memory contents}
•{OPT} ... {optimizes solution memory}
•{DISP} ... {displays solution memory contents}

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7-1-9
Using the CAS (Computer Algebra System) Mode
uTo save a calculation history to solution memory (Save)
On the initial solution memory screen, press 1(SAVE).
Press 1(YES) to save the calculation history to solution memory.
Pressing ireturns to the solution memory initial screen.
•Pressing 6(NO) in place of 1(YES) returns to the solution memory initial screen without
saving anything.
uTo clear solution memory contents (Clear Memory)
On the initial solution memory screen, press 2(DEL
•
A).
Press 1(YES) to clear solution memory contents.
Pressing ireturns to the solution memory initial screen.
•Pressing 6(NO) in place of 1(YES) returns to the solution memory initial screen without
clearing anything.
•This clears both CAS Mode and ALGEBRA Mode memory contents. You cannot select the
mode shows memory contents you want to delete.

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•6(DISP) is disabled when there is no data in Solution memory.
•To display the next record
Press 6(NEXT).
•To display the previous record
Press 1(BACK).
•Pressing 1(BACK) while the oldest record is on the display returns to the solution
memory initial screen.
•To display a particular record
Press 5(SEL) and then input the number of the record you want to display.
Pressing wdisplays the record whose number you input.
•To delete a single solution memory record
Display the record you want to delete, and then press 2(DEL).
In response to the confirmation message that appears, press w(Yes) to delete the record
you displayed.
To clear the above screen without deleting anything, press i(No).
•To toggle record number display on and off
Press 4(NUM) to toggle display of the record number on and off.
uTo optimize solution memory (Optimization)
On the initial solution memory screen, press 3(OPT).
Pressing ireturns to the solution memory initial screen.
Optimizing solution memory rearranges data and can free up more storage space. Perform
the above procedure when solution memory capacity starts running low.
7-1-10
Using the CAS (Computer Algebra System) Mode
uTo display solution memory contents (Display Memory)
On the initial solution memory screen, press 6(DISP).
This displays the oldest expression and result in solution memory. The bottom line shows the
record number.

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7-1-11
Using the CAS (Computer Algebra System) Mode
Algebra Command Reference
The following are the abbreviations used in this section.
•Exp ... Expression (value, formula, variable, etc.)
•Eq ... Equation
•Ineq ... Inequality
•List ... List
•Mat ... Matrix
•Vect ... Vector
Anything enclosed within square brackets can be omitted.
uexpand
Function: Expands an expression.
Syntax: expand ( {Exp/Eq/Ineq/List/Mat/Vect} [ ) ]
○○○○○
Example To expand (X+2)2
1(TRNS)b(expand)(v+c)xw X2+ 4X + 4
urFactor (rFctor)
Function: Factors an expression up to its root.
Syntax: rFactor ( {Exp/Eq/Ineq/List/Mat/Vect} [ ) ]
○○○○○
Example To factor the X2– 3
1(TRNS)c(rFctor)vx-dw(X – 3) (X + 3)
ufactor
Function: Factors an expression.
Syntax: factor ( {Exp/Eq/Ineq/List/Mat/Vect} [ ) ]
○○○○○
Example To factor X2– 4X + 4
1(TRNS)d(factor)vx-ev+ew(X – 2)2

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usolve
Function: Solves an equation.
Syntax: solve( Eq [,variable] [ ) ]
solve( {Eq-1,..., Eq-n}, {variable-1,...,variable-n} [ ) ]
○○○○○
Example To solve AX + B = 0 for X
1(TRNS)e(solve)av(A)v+
al(B)!.(=)aw
○○○○○
Example To solve simultaneous linear equation 3X + 4Y = 5, 2X – 3Y = – 8
1(TRNS)e(solve)!*( { )
da+(X)+ea-(Y)!.(=)f,
ca+(X)-da-(Y)!.(=)-i
!/( } ),!*( { )a+(X),X = – 1
a-(Y)!/( } )wY = 2
• X is the default when no variable is specified.
utExpand (tExpnd)
Function: Employs the addition theorem to expand a trigonometric function.
Syntax: tExpand( {Exp/List/Mat/Vect} [ ) ]
○○○○○
Example To employ the addition theorem to expand sin(A+B)
1(TRNS)f(TRIG)b(tExpnd)
s(av(A)+al(B)wcos(B) • sin(A) + sin(B) • cos(A)
utCollect (tCollc)
Function: Employs the addition theorem to transform the product of a trigonometric
function to a sum.
Syntax: tCollect( {Exp/List/Mat/Vect} [ ) ]
○○○○○
Example To employ the addition theorem to transform sin(A)cos(B) to
trigonometric sum
1(TRNS)f(TRIG)c(tCollc)
sav(A)cal(B)w
7-1-12
Using the CAS (Computer Algebra System) Mode
sin (A + B)
2
sin (A – B)
2
+
– B
A
X =
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7-1-13
Using the CAS (Computer Algebra System) Mode
utrigToExp (trigToE)
Function: Transforms a trigonometric or hyperbolic function to an exponential function.
Syntax: trigToExp( {Exp/List/Mat/Vect} [ ) ]
○○○○○
Example To convert cos(iX) to an exponential function
1(TRNS)f(TRIG)d(trigToE)c!a(i)vw
uexpToTrig (expToT)
Function: Converts an exponential function to a trigonometric or hyperbolic function.
Syntax: expToTrig( {Exp/List/Mat/Vect} [ ) ]
○○○○○
Example To convert eix to a trigonometric function
1(TRNS)f(TRIG)e(expToT)
!I(ex)(!a(i)vw cos(X) + sin(X) •i
usimplify (smplfy)
Function: Simplifies an expression.
Syntax: simplify( {Exp/Eq/Ineq/List/Mat/Vect} [ ) ]
○○○○○
Example To simplify 2X + 3Y – X + 3 = Y + X – 3Y + 3 – X
1(TRNS)g(smplfy)ca+(X)+da-(Y)
-a+(X)+d!.(=)a-(Y)
+a+(X)-da-(Y)+d-
a+(X)wX + 3Y + 3 = –2Y + 3
ex+ e
—
x
2

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ucombine (combin)
Function: Adds and reduces rational expressions.
Syntax: combine( {Exp/Eq/Ineq/List/Mat/Vect} [ ) ]
○○○○○
Example To reduce the fraction (X + 1) / (X + 2) + X (X + 3)
1(TRNS)h(combin)(v+b)/
(v+c)+v(v+dw
ucollect (collct)
Function: Rearranges an expression, focusing on a particular variable.
Syntax: collect( {Exp/Eq/Ineq/List/Mat/Vect} [,{Exp/variable}] [ ) ]
○○○○○
Example To rearrange X2+ AX + BX, focusing on the variable X
1(TRNS)i(collct)vx+av(A)v+
al(B)vw X2+ (A + B)X
• X is the default when nothing is specified for [,{Exp/variable}].
usubstitute (sbstit)
Function: Assigns an expression to a variable.
Syntax: substitute( {Exp/Eq/Ineq/List/Mat/Vect}, variable=expression
[,..., variable=expression] [ ) ]
○○○○○
Example To assign 5 to X in 2X – 1
1(TRNS)j(sbstit)cv-b,
v!.(=)fw9
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Using the CAS (Computer Algebra System) Mode
X3+ 5X2+ 7X + 1
X + 2
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ucExpand (cExpnd)
Function: Expands xth root of imaginary number.
Syntax: cExpand( {Exp/Eq/Ineq/List/Mat/Vect} [ ) ]
○○○○○
Example To expand 2i
1(TRNS)v(cExpnd)!x( )c!a(i)w1 + i
uapprox
Function: Produces a numerical approximation for an expression.
Syntax: approx( {Exp/Eq/Ineq/List/Mat/Vect} [ ) ]
○○○○○
Example To obtain a numerical value for 2
1(TRNS)l(approx)!x( )cw1.414213562
○○○○○
Example 920
Normal:jMcaw12157665459056928801
approx: 1(TRNS)l(approx)jMcaw1. 215766546E+19 (Display: Norm1)
7-1-15
Using the CAS (Computer Algebra System) Mode
#About approx
With normal calculations (when approx is not
used) in the CAS Mode, calculation results are
displayed in full, without using exponents.
When you use approx in the CAS Mode,
however, results are displayed using the
exponential format range specified by the Display
item of the SET UP screen.
This means approx displays results in the CAS
Mode the same way they are displayed in the
RUN•MAT Mode.

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udiff
Function: Differentiates an expression.
Syntax: diff( {Exp/List} [, variable, order, derivative] [ ) ]
diff( {Exp/List}, variable [, order, derivative] [ ) ]
diff( {Exp/List}, variable, order [, derivative] [ ) ]
○○○○○
Example To differentiate X6with respect to X
2(CALC)b(diff)vMgw6X5
• X is the default when no variable is specified.
• 1 is the default when no order is specified.
u∫
Function: Integrates an expression.
Syntax: ∫( {Exp/List} [, variable, integration constant] [ ) ]
∫( {Exp/List}, variable [, integration constant] [ ) ]
∫( {Exp/List}, variable, lower limit, upper limit [ ) ]
○○○○○
Example To integrate X2with respect to X
2(CALC)c(∫ )vxw
• X is the default when no variable is specified.
ulim
Function: Determines the limits of a function expression.
Syntax: lim( {Exp/List}, variable, point [, direction] [ ) ]
○○○○○
Example To determine the limits of sin(X)/X when X = 0
2(CALC)d(lim)sv/v,v,aw1
• Direction can be positive (from right) or negative (from left).
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Using the CAS (Computer Algebra System) Mode
X3
3

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uΣ
Function: Calculates a sum.
Syntax: Σ( {Exp/List}, variable, start value, end value [ ) ]
○○○○○
Example To calculate the sum as the value of X in X2changes from X = 1
through X = 10
2(CALC)e(Σ)vx,v,b,baw385
uΠ
Function: Calculates a product.
Syntax: Π( {Exp/List}, variable, start value, end value [ ) ]
○○○○○
Example To calculate the product as the value of X in X2changes from X = 1
through X = 5
2(CALC)f(Π)vx,v,b,fw14400
utaylor
Function: Finds a Taylor polynomial.
Syntax: taylor( {Exp/List}, variable, order [, center point] [ ) ]
○○○○○
Example To find a 5th order Taylor polynomial for sin(X) with respect to X = 0
2(CALC)g(taylor)sv,v,f,aw
•The default center point is zero.
uarcLen
Function: Returns the arc length.
Syntax: arcLen( {Exp/List}, variable, start value, end value [ ) ]
○○○○○
Example To determine the arc length for X2from X = 0 to X = 1
2(CALC)h(arcLen)
vx,v,a,bw
7-1-17
Using the CAS (Computer Algebra System) Mode
X5
–X3+X
120 6
In (4 5 + 8) –In(2) + 5
422

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utanLine (tanLin)
Function: Returns the expression for a tangent line.
Syntax: tanLine( {Exp/List}, variable, variable value at point of tangency [ ) ]
○○○○○
Example To determine the expression for a line tangent with X3when X = 2
2(CALC)i(tanLin)vMd,v,cw12X – 16
udenominator (den)
Function: Extracts the denominator of a fraction.
Syntax: denominator( {Exp/List} [ ) ]
○○○○○
Example To extract the denominator of the fraction (X + 2)/(Y – 1)
2(CALC)j(EXTRCT)b(den)
(a+(X)+c)/(a-(Y)-bwY – 1
unumerator (num)
Function: Extracts the numerator of a fraction.
Syntax: numerator( {Exp/List} [ ) ]
○○○○○
Example To extract the numerator of the fraction (X + 2)/(Y – 1)
2(CALC)j(EXTRCT)c(num)
(a+(X)+c)/(a-(Y)-bwX + 2
ugcd
Function: Returns the greatest common divisor.
Syntax: gcd( {Exp/List}, {Exp/List} [ ) ]
○○○○○
Example To determine the greatest common divisor of X + 1 and X2– 3X – 4
2(CALC)v(gcd)v+b,vx-
dv-ewX + 1
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Using the CAS (Computer Algebra System) Mode
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ulcm
Function: Obtains the least common multiple of two expressions
Syntax: lcm( {Exp/List}, {Exp/List} [ ) ]
○○○○○
Example To obtain the least common multiple of X2– 1 and X2+ 2X – 3
2(CALC)l(lcm)vx-b,
vx+cv-dwX3+ 3X2– X – 3
urclEqn
Function: Recalls multiple eqn memory contents.
Syntax: rclEqn( memory number [, ..., memory number] [ ) ]
○○○○○
Example To recall the contents of equation memory 2 and equation memory 3
3(EQUA)c(rclEqn)c,dw3X –Y = 7
3X + 6Y = 63
•The memory numbers of equations produced as the result of a recall are not updated.
urclAllEqn (rclAll)
Function: Recall all eqn memory contents.
Syntax: rclAllEqn
•The memory numbers of equations produced as the result of a recall are not updated.
urewrite (rewrit)
Function: Moves the right side expression to the left side.
Syntax: rewrite( {Eq/Ineq/List} [ ) ]
○○○○○
Example To move the right side expression of X + 3 = 5X – X2to the left side
3(EQUA)e(rewrit)v+d!.(=)
fv-vxw X2– 4X + 3 = 0
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Using the CAS (Computer Algebra System) Mode
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